Theorems · Theorem · commutative algebra

Module.FaithfullyFlat.rTensor_exact_iff_exact

∀ (R : Type u) (M : Type v) [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {N1 : Type u_1}
  [inst_3 : AddCommGroup N1] [inst_4 : Module R N1] {N2 : Type u_2} [inst_5 : AddCommGroup N2] [inst_6 : Module R N2]
  {N3 : Type u_3} [inst_7 : AddCommGroup N3] [inst_8 : Module R N3] (l12 : N1 →ₗ[R] N2) (l23 : N2 →ₗ[R] N3)
  [Module.FaithfullyFlat R M],
  Function.Exact ⇑(LinearMap.rTensor M l12) ⇑(LinearMap.rTensor M l23) ↔ Function.Exact ⇑l12 ⇑l23

Defined in: Mathlib.RingTheory.Flat.FaithfullyFlat.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module AddCommGroup Module AddCommGroup Module AddCommGroup Module Module.FaithfullyFlat

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DFunLike.coestatement and proof · cited by 62,936
Modulestatement and proof · cited by 20,661
RingHom.idstatement and proof · cited by 18,349
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
LinearMapstatement and proof · cited by 10,215
TensorProductstatement · cited by 2,545
LinearMap.rTensorstatement and proof · cited by 266
Function.Exactstatement and proof · cited by 182
Module.FaithfullyFlatstatement and proof · cited by 72
Module.Flat.rTensor_exactproof · cited by 3
Module.FaithfullyFlat.rTensor_reflects_exactproof · cited by 2

Cited by1

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Module.FaithfullyFlat.iff_exact_iff_rTensor_exactproof · cited by 0